In his invitingly-entitled May 1997 article, "Inverse Pressure Gradient Matching," Mike Arnold brought up some interesting points about controlling interference drag. I thought his ideas might have reached a larger audience if he had called the piece "Bulges in All the Right Places" or something like that, but never mind. One of his suggestions was that interference could be reduced by staggering the fat parts of an airplane, in a manner similar to the way area-ruling is used to reduce transonic drag. This notion was also endorsed by the late John Thorp, designer of the T-18, who called it his "poor man's area rule." Mike discussed canopy placement at some length, suggesting that the bulge of the canopy ought to be placed either well ahead of or well behind the point of maximum thickness of the

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wing. I was inspired by his comments

to run a few computer analyses in order to see whether the effects he predicted would show up. The computer program I used is AeroLogic's PSW. (I am a partner in AeroLogic.) PSW's method is similar to that of VSAERO, with which David Lednicer performs the analyses of various sport planes that have appeared recently in Sport Aviation. Readers who have followed Lednicer's articles, with their rainbow-hued illustrations, know that this class of software applies basic laws of fluid motion to air flowing over a 3-dimensional numerical model of an airplane, and predicts pressure distribution, loads, and boundary-layer characteristics, including skin friction. Since it can deal with multi-body geometries of arbitrary complexity, it is a good tool for investigating interference effects. Let's start by considering what interference drag is. It arises from several mechanisms. Two that interest us here are 1) increased surface friction due to acceleration produced by a 'Venturi" effect that occurs when streamlined objects are near one another; and 2) premature separation due to overly 66

rapid deceleration of the flow after

passing the objects. Some interferences are unavoidable, but Mike's idea is that it should be possible to reduce interference drag by adjusting the locations of components. A good example is the "waisting" of the aft fuselage of the Citation X. Scooping away some of the fuselage next to the pylon-mounted engines reduces velocities in the passage between them, and so cuts down on friction drag and helps to make the Citation X the fastest of corporate jets. In his article, Mike gave a lot of attention to canopy placement with respect to the wing. To test his thesis, which was that the canopy should be generally aft of the wing, I created a small, simple airplane model (Figure 1) and analyzed three different canopy placements. It turned out that the properties of the middle one were intermediate between those of the front and rear, and so I'll henceforth omit it from the discussion. I'll call the rearcanopy version R and the other F. To start with, I was curious what effect the canopy had on streamline paths along the side of the airplane. Figure 2 shows a set of streamlines along the

sides of F and R. As you would expect, moving the canopy forward pushes the nearby streamlines downward, and also slightly increases the flow velocity over the wing root. These are exactly the interference effects Mike warned of. Once aft of the wing and canopy the streamlines return to approximately the same paths in both configurations. Near the tail, however, the boundary layer is about .35 in. thicker on F than on R, suggesting, as Mike argued, that R should produce less drag. So far as skin friction is concerned, however, PSW found little difference between the two configurations. At about 200 mph, F had 65.8 pounds of skin friction drag and R had 64.6. Since F has 2.5% more wetted area than R, this difference is inconsequential; but it does suggest that interference between the wing and the canopy is really not a big element in the total drag. In fact, if the canopy were a bubble and F did not have a turtledeck, there would be no significant difference in skin friction between the two configurations at all. Having obtained this surprising result, I looked at the pressure distribution on the upper surfaces of the wings near

the roots in order to see what the effect of canopy position was. PSW allows

you to compare two models by mapping the difference in pressure between them. Figure 3 shows such a difference map. Green indicates no difference in pressure; blue indicates higher pressure (less lift) — and red indicates lower pressure (more lift). It's immediately apparent that in addition to making its own lift contribution, F's canopy increases the wing's lift. This suggests a new question: Apart from reducing interference drag, what unintended consequences, good or bad, might an aft canopy position have? Figure 4 compares the spanwise upper-surface pressure distributions for F and R. (Only one half of the span is illustrated.) As you would expect, R shows a deep trough across the fuselage, whereas F maintains lift better in that area because the canopy itself has a somewhat a i r f o i l - l i k e shape. The predicted lift coefficients for the complete airplanes shows the effect of this trough: F produces 8% more lift than R at the same angle of attack. Since both models are presumably being flown at the same weight, I reduced the angle of attack of F by about a quarter of a degree and repeated the analysis (which takes about 3 minutes on a 90 MHz Pentium). Now the lift coefficients were almost exactly the same, but the F's span efficiency (or e) was nearly 7% higher and its induceddrag coefficient about 7% lower. As you know, induced drag, which is the drag associated with the production of lift, is inversely proportional to the square of indicated airspeed. Thus, it is a comparatively minor factor in cruise at low altitude for conventional airplanes, but becomes significant when climbing, gliding, flying for long range,

and purposes to them. But to the passing air, they are all parts of a single undifferentiated blob. As designers, we strive for the blob that yields the

most lift for the least drag. But lift and drag are two ways of integrating a single pressure field; we cannot consider them in isolation from one another. +

cruising at high altitude, or pulling G's.

For pylon racing, for instance, where speed lost during pylon turns is critical, the tradeoff between the skin friction benefits and the induced-drag penalties of an aft canopy position would merit more detailed investigation. This analysis, though quick and superficial, shows that ideas like the "poor man's area rule" can have unexpected ramifications, and in practice may not yield the expected results. When we look at an airplane we see a collection of distinct entities called "wing," "fuselage," "canopy" and so

on, and we assign different properties 67